To prove well-posedness, we follow the general setting presented in [1]} which relies on the application of the Banach-Nečas-Babuška Theorem.
The form considered in [1]} is given in an operator formulation as
\(\begin{split}L \partial ^\bullet _\phi {u} + Au + \Lambda u &= f \mbox{ in } L^2_{V^*},\\u(0) &= u_0 \in H_0,\end{split}\qquad \mathrm {(\textbf {P})}\) 
